This paper presents a numerical model for addressing thermo-mechanical coupling problems in topology optimization, utilizing the element-free Galerkin (EFG) method. A multi-parameter density-based topology optimization framework is introduced to interpolate the thermal stress coefficient, encompassing thermal conductivity, thermal expansion coefficient, and elastic modulus. Two numerical examples are provided to investigate the model's characteristics and associated considerations, including the impact of EFG node distribution, quantity, calculation points layout, design variables, and filtering techniques on optimized results. Numerical findings indicates that the present model allows for adaptable adjustments in nodes number and distribution, calculation points layout, choice of design variables, and application of various filtering techniques while maintaining consistent background grids. Although these adjustments may affect convergence rates and final objective values, they can promise satisfactory optimization structures. Additionally, the study highlights the critical influence of filtering radius on optimization outcomes and the objective value, recommending a value of approximately 16∼20 calculation points.

中文翻译：

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使用无单元伽辽金方法最小化热机械载荷下的平均柔量的拓扑优化


本文提出了一种利用无单元伽辽金 (EFG) 方法解决拓扑优化中的热机耦合问题的数值模型。引入了基于密度的多参数拓扑优化框架来插值热应力系数，包括热导率、热膨胀系数和弹性模量。提供了两个数值示例来研究模型的特征和相关考虑因素，包括 EFG 节点分布、数量、计算点布局、设计变量和过滤技术对优化结果的影响。数值结果表明，本模型允许对节点数量和分布、计算点布局、设计变量的选择以及各种过滤技术的应用进行适应性调整，同时保持一致的背景网格。尽管这些调整可能会影响收敛速度和最终目标值，但它们可以保证令人满意的优化结构。此外，研究强调了过滤半径对优化结果和目标值的关键影响，建议计算点的值约为16∼20个。